Problem: Solve for $x$ and $y$ using elimination. ${-5x-3y = -75}$ ${-4x+3y = -6}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $-9x = -81$ $\dfrac{-9x}{{-9}} = \dfrac{-81}{{-9}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-5x-3y = -75}\thinspace$ to find $y$ ${-5}{(9)}{ - 3y = -75}$ $-45-3y = -75$ $-45{+45} - 3y = -75{+45}$ $-3y = -30$ $\dfrac{-3y}{{-3}} = \dfrac{-30}{{-3}}$ ${y = 10}$ You can also plug ${x = 9}$ into $\thinspace {-4x+3y = -6}\thinspace$ and get the same answer for $y$ : ${-4}{(9)}{ + 3y = -6}$ ${y = 10}$